I have an 1999 F350 Dually that I use to tow my 31ss. I'm thinking about having a 6" suspension lift put on with 35" tires. Will this hurt my towing ability?

A little different situation, but I tow my dads 26 (guess 2000# lighter) with my 2500HD crew cab 8.1L 6" procomp lift every weekend. The lift had no negative effects at all.

If you have the 7.3 Powerstroke, u will not have any issues. Just get a drop hitch to level the trailer.

Short answer....yes. Lots more rotating mass. You really should lower the axle ratio to compensate for the larger tires. Even if your rig puts out plenty of power, you are stressing trans, axles, t-case by requiring more go-pedal to turn the larger tires. The truck will feel lots more peppy with some deeper gears too.